Shot noise distributions and selfdecomposability

2001/11/07 by Aleksander M. Iksanov, Iksanov, Aleksander M., Zbigniew J. Jurek +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.math/0111069

14 pages, accepted for publication

arxiv created 2002/10/25 · arxiv updated 2009/11/30

Abstract

Stationary (limiting) distributions of shot noise processes, with exponential response functions, form a large subclass of positive selfdecomposable distributions that we illustrate by many examples. These shot noise distributions are described among selfdecomposable ones via the regular variation at zero of their distribution functions. However, slow variation at the origin of (an absolutely continuous) distribution function is incompatible with selfdecomposability and this is shown in three examples.

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